Optical dielectric properties of HfO₂-based films

Beyond the use of HfO₂ as a high-k dielectric material in the semiconductor industry,^1–4 the recent discovery of ferroelectricity and resistive switching in HfO₂ and its compounds opens the use of this material system for further applications in microelectronics.^5–9 Compounds based on HfO₂, including Y-doped HfO₂ (HYO), Zr-doped HfO₂ (HZO), and Ce-doped HfO₂ (HCO), have drawn increasing attention in recent years because of the possibility to control the crystal structure and thus improve the electrical properties of HfO₂.^10–16 There are only a few studies on the optical response of the HfO₂-based films at higher frequencies relevant for optical applications.^17–19 Despite the opportunity to use doping to tailor the refractive index, which is an important property in determining the focusing power of lenses and the light-guiding nature of optical fibers, the characterization of solid solutions of HfO₂-based compounds is still largely missing.

In this paper, we evaluate the dielectric constant of HfO₂-based films of selected compounds on MgO (001) substrates. The structures of these films are characterized using x-ray diffraction (XRD) and transmission electron microscopy (TEM). We find that the 20 mol. % Y-doped HfO₂ (HYO) film stabilizes in the cubic phase, the Hf_0.5Zr_0.5O₂ (HZO) film stabilizes predominantly in the monoclinic phase with regions in the cubic phase, and the Hf_0.5Ce_0.5O₂ (HCO) film stabilizes predominantly in the cubic phase with regions in the monoclinic phase. We discuss the roles of phase change under doping and refractive index of a solid solution individually for each film to account for our observations. The optical dielectric constant is found here to be the lowest in HYO films, intermediate in HZO films, and highest in HCO films. The dielectric constant is found to be higher in films doped with material of a higher dielectric constant. Our findings show that the dielectric constant can be tuned by incorporating constituent materials with different dielectric constants, which is of interest in optoelectronic devices.

Films of HYO, HZO, and HCO were deposited on (001)-oriented MgO substrates via pulsed laser deposition (PLD) using a KrF excimer laser (λ = 248 nm) operating at a repetition rate of 5 Hz. The MgO substrate was chosen because of its low dielectric constant to minimize the complexity in optical analysis.²⁰ A substrate temperature of 800 °C, oxygen pressure of 25 mTorr, and laser fluence of 1 J/cm² were used during deposition. After deposition, the films were cooled in an oxygen atmosphere of 200 Torr without any further in situ thermal treatment. The structural characterization of all three films was done by x-ray diffraction (XRD) and transmission electron microscopy (TEM). The thickness of our films is determined as an average value of ten points across each film measured from TEM. Optical responses of the samples were measured using a J. A. Woollam VASE ellipsometer and further analyzed using the CompleteEASE software from the same company.

We first characterize the structure of the samples using XRD, see Fig. 1. For the HYO film, only the diffraction peaks (⁠$111$⁠) and (⁠$222$⁠) of the cubic phase are observed in the Θ-2Θ scan. For the HZO and HCO films, several additional peaks appear in the Θ-2Θ scan, which suggests incorporation of additional phases in the film such as the orthorhombic and cubic phase in HZO, and cubic phase in HCO. The peak positions of our HfO₂-based solid solutions differ with respect to HfO₂ in peak positions in XRD because of the different ionic radii of dopant materials, as shown in Table I. The XRD pattern of HfO₂ is expected to best match with the XRD pattern for the HZO films because of the similar ionic radius and smaller crystallite size. Both Y³⁺ ions and Ce⁴⁺ ions are about 25% larger than the Hf⁴⁺ and Zr⁴⁺ ions. Doping with either Y₂O₃ or CeO₂ is thus expected to result in an increase in lattice parameters of HfO₂ and thus a downward shift of 2Θ values. Besides the larger lattice parameter of Y₂O₃ and the larger Y³⁺ ions, the smaller coordination number of Y³⁺ cations induces oxygen vacancies and therefore introduces more complexity to the consequent refractive index. The change in the electron density as a result of the charge compensation for the incorporation of oxygen vacancies and also the phase changes are all possible contributing factors to the aforementioned complexity. The discrepancy to the pure HfO₂ for our films is expected to be smaller for HYO than for HCO because of the smaller amount of the Y dopant with respect to Ce dopant.

Since the XRD analysis is complex as described above, we have used the TEM technique to make final conclusions on the phase composition. The diffraction patterns and local fast Fourier transforms (FFT) captured in the microscopic images provide more information about crystal planes other than the out-of-plane directions. For the HYO film, the thickness is found to be 84 ± 2 nm. The textured growth of HYO on top of the MgO substrate is further confirmed by the sharp interface between HYO and MgO, as shown in Figs. 2(a) and 2(b). Electron diffraction shown in Fig. 2(c) further confirms the stabilization of cubic HYO. STEM image in Fig. 2(d) shows uniform growth of HYO on the MgO substrate. Complete mixing and uniform distribution of Y and Hf are shown in the energy dispersive spectroscopic (EDS) mapping in Figs. 2(e)–2(g). The cubic phase HYO found in our 20% Y:HfO₂ is in agreement with the results shown in the previous report on the crystal structures of bulk Y:HfO₂ with 20% Y doping concentration.²⁴ 

For the HZO film, the thickness is found to be 145 ± 1 nm. The morphology of HZO films is drastically different in comparison to the HYO films. In Fig. 3(a), clear contrast between regions of different phases can be observed. The different crystal structures can be identified in magnified images in Figs. 3(b) and 3(d). The HZO films are predominantly in the monoclinic phase, in contrast to HYO, with inclusions of the cubic phase. Electron diffraction in Fig. 3(c) shows the presence of multiple sets of diffraction patterns suggesting the incorporation of multiple phases and different orientations in the film. Complete mixing and uniform distribution of Hf and Zr are shown in the energy dispersive spectroscopic (EDS) mapping in Figs. 3(e)–3(g).

For the HCO film, the thickness is found to be 69 ± 0.7 nm. Two different crystal structures, cubic and monoclinic, are observed in the TEM and STEM images, as shown in Figs. 4(a), 4(b), and 4(d). Electron diffraction shown in Fig. 4(c) confirms the presence of monoclinic phase grains with mirrored orientations. The presence of monoclinic and cubic phase is in agreement with previous reports of HCO films for large crystallite sizes and with no/little concentration Ce³⁺ (Refs. 25–27). EDS mapping of the HCO film shown in Figs. 4(e)–4(g) also suggests complete mixing of Hf and Ce.

We now move onto the optical characterization of HYO, HZO, and HCO films and later discuss the results with regards to structural characterization and dopant properties. A J. A. Woollam VASE ellipsometer was used to measure the perpendicular (R_s) and parallel (R_p) (with respect to the plane of incidence) reflection coefficients of the sample in the range from 300 to 2000 nm. The ratio of these reflection coefficients defines the two parameters, $Ψ$ and $Δ$⁠, at a given wavelength and incidence angle, by Eq. (1),

$Ψ$ and $Δ$ data are shown in Figs. 5(a)–5(c) in red and green lines at 5 different incident angles (30°, 40°, 50°, 60°, 70°), respectively. The results of the corresponding $Ψ$ and $Δ$ are fitted with a mathematical model consisting of a B-spline bi-axial layer for film simulation and a MgO substrate from the J. A. Woollam's material library. The fits match the raw data with a mean-square error (MSE) around 5, indicating that the fitting model is properly selected. Thicknesses obtained from the fitting results are 97.68, 116.79, and 69.54 nm for HYO, HZO, and HCO, respectively, are in good agreement with the thicknesses derived directly from TEM and STEM images. This fitting results offer a reference for future (in situ) thickness estimation of HfO₂-based compounds using optical characterization. The permittivity results (real part $εr$ and imaginary part $εi$⁠), shown in Fig. 5(d), are derived by fitting the ellipsometric $Ψ$ and $Δ$ data using the general oscillator (Gen-Osc) model to enforce the Kronig consistency, which ensures the realistic shape of the optical dispersion.

The lowest real permittivity is observed in the HYO films, with dispersion from 5.07 at 300 nm to 4.27 at 2000 nm. An intermediate real permittivity is found in the HZO film, where the value of permittivity varies from 5.39 at 300 nm to 4.33 at 2000 nm. The feature found at around 500 nm in HZO film is associated with the increase in absorption loss potentially due to the interaction between the incident beam and vertical phases and grains in the HZO sample. HCO film shows the highest real permittivity with the largest dispersion from 7.66 at 300 nm to 4.71 at 2000 nm. The refractive index n and extinction coefficient k are directly related to the real part of the dielectric permittivity (⁠$εr$⁠) by the following equation: $εr=n2−k2$⁠. For transparent oxide thin films, the extinction coefficient k is usually several orders of magnitude smaller than n. Thus, the real dielectric permittivity $εr$ can be estimated by the value of n by $εr≈n2$⁠. We thus estimate the refractive indices in the measured wavelength range (300–2000 nm) to be 2.25–2.07, 2.32–2.08, 2.77–2.17, for HYO, HZO, and HCO, respectively.

We relate the optical properties (relative permittivity) of our films to their crystal structure and dopant materials. Relative permittivity of a system depends on its molar polarizability and molar volume, which are determined by the composition, phase, and crystallinity (density).³¹ Properties of thin films additionally depend on the growth parameters, substrate, thickness, etc., For a solid solution, relative permittivity can be approximated by a weighted average of the relative permittivities of the two constituent materials in the simplest scenario. An addition of a dopant material can, however, provoke phase changes in the host material resulting in a drastically different relative permittivity than the equilibrium phase of the host. In the case of phase change upon doping, it is difficult to disentangle the effects of (1) mixing of two materials with different relative permittivities and (2) phase change upon doping, on the relative permittivity of the final material. We thus compare the trend of the measured refractive indices with the expected trends depending on the crystal structure and the dopant material. To interpret the fitting results, we consider previous studies on the value of refractive index in HfO₂ and corresponding dopants. We summarize the comparison for refractive index at 600 nm in Table II.

In experimental studies of HfO₂ films in the monoclinic phase, refractive index of 2.38–2.12 (Ref. 23) and 2.2–2.1 (Ref. 22) has been reported in the wavelength range of 300–2000 nm. The refractive index attributed to the electronic contributions has been calculated by Kumar et al.³² in the wavelength range of 300–2000 nm to be 2.35/2.18–1.96/1.87 for the xx/zz components of the monoclinic phase and 2.54–2.02 for the cubic phase at 600 nm. In the case of mixed-phase samples, addition of cubic regions to a (nominally) monoclinic sample is expected to lead to an increase in the measured refractive index and more dispersion.

Furthermore, the refractive indices of dopants in the wavelength range of 300–2000 nm are 2.38–2.12 for HfO₂,²⁸ 2.0–1.8 for Y₂O_3,²⁹ 2.52–2.16 for ZrO₂,²⁸ and 2.8–2.2 for CeO₂.³⁰ It is expected that an intermediate refractive index value would be achieved in doped films according to the constituent compounds. The higher refractive index and more dispersion is observed in the films with dopants with higher refractive index and more dispersion.

Both the trend of the refractive index of constituent crystal structures and the refractive index of dopants match the trend of the refractive index observed in the corresponding films. Incorporating constituents with higher refractive indices can therefore tailor the refractive indices of the corresponding compounds effectively through crystal structure and electronic structure. In future studies, separating the contributions of crystal structure and dopants could be possible if one could control either of the parameters independently.

In summary, we compared the optical dielectric constant of HfO₂-based films of HYO, HZO, and HCO films on MgO substrates. We found that while the HYO film is stabilized in the cubic phase, the HZO films is stabilized in the monoclininc phase with partial incorporation of the cubic phase, and HCO is stabilized in the cubic phase with partial incorporation of the monoclinic phase. The optical permittivity of the films reveals the electronic contribution to the overall dielectric properties and a trend of higher permittivity for films with constituent phases and dopants of higher permittivity. Considering the significance of dielectric properties of HfO₂-based materials at optical frequencies, future directions should be centered around films grown on more prevalent substrates in the industry such as silicon,³³ which will provide crucial information for studies on the HfO₂-based devices for optoelectronic applications.

The U.S.–U.K. collaborative effort was funded by the U.S. National Science Foundation No. ECCS-1902644 (Purdue University), No. ECCS-1902623 (University at Buffalo, SUNY)] and the EPRSC Grant No. EP/T012218/1. J.L.M.-D. and N.S. acknowledge support from the Swiss National Science Foundation under Project No. P2EZP2-199913 and the ERC Grant No. U-H2020-ERC-ADG No. 882929, EROS. J.L.M.-D. also acknowledges support from the Royal Academy of Engineering (Grant No. CIET1819_24).

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.